# Series grouping

• Same current flows through each resistance but potential difference distributes in the ratio of resistance, i.e., V R

Fig. 13
• Equivalent resistance is greater than the maximum value of resistance in the combination, i.e., Req = R1 + R2 + R3.
• If n identical resistance are connected in series Req = nR and potential difference across each resistance V’ = V/n.

# Parallel grouping

• Same potential difference appeared across each resistance but current distributes in the reverse ratio of their resistance, i.e., i ∝ 1/R.

Fig. 14
• Equivalent resistance is given by

or

Equivalent resistance is smaller than the minimum value of resistance in the combination.
• If two resistances in parallel,

• Current through any resistance,

where i’ = required current (branch current), i = main current and

Fig. 15
• In n identical resistance are connected in parallel Req = R/n and current through each resistance i’ = i/n.
Notes:
• If n identical resistances are first connected in series and then in parallel, the ratio of the equivalent resistance is given by .
• If equivalent resistance of R1 and R2 in series and parallel be Rs and Rp, respectively, then

and

If a wire of resistance R is cut in n equal parts and then these parts are collected to form a bundle, then equivalent resistance of combination will be R/n2.